What is wrong with the idea that the AI will be capable of omniscience?
I quite like your outlook, and without getting into the details of how a "singularity" may be effected which is covered in numerous other questions, or how consciousness and "omniscience" come into play because consciousness and omniscience are not requirements, I will instead direct you to two key philosophers:


Phillip K. Dick, for whom the central theme in his famous 1968 book on AI is empathy.  (If you haven't read it, I'm not posting a spoiler, but will only say the plot is driven by the concept of Evolutionary Game Theory which was formalized just 5 years later.) 
John Nash, and in particular, the concept of the Nash Equilibrium. (Nash could be said to have mathematically demonstrated that being a "douchebag" is not an optimal strategy.  His proof can be used to explain why nuclear détente actually worked, which was counter to the expectation of Von Neumann.) 


So when people go nuts, focusing on the "Skynet" mythos under which machines rise up to destroy us, I have to wonder if they're simply not as smart as Nash or as profound as Dick, which might explain their lack of emphasis on what can be called the "Electric Sheep" paradigm.